Name: Jay Goyal¶

Roll No: C017

Btech EXTC

Experiment-5

Aim:

1. Observe frequency components of audio files using FFT
2. To filter low and high frequency components using low and high pass filter

Mam method

from scipy.io import wavfile
from IPython.display import Audio
import numpy as np
import matplotlib.pyplot as plt

fs1, data1 = wavfile.read(r'C:\Users\JAY GOYAL\Forest.wav')
Audio(data=data1, rate=fs1)

print("sampling frequency: ",fs1)
plt.plot(data1)
plt.xlabel("n -->")
plt.ylabel("Amplitude -->")

sampling frequency:  44100

Text(0, 0.5, 'Amplitude -->')

from scipy import signal               #Mam method
fs = 1000
t = np.arange(1000)/fs
signals = np.sin(2*np.pi*100*t)
plt.figure(figsize=(20,4))
plt.title("Signal A")
plt.plot(t,signals)
plt.xlabel("Frequency", color='r')
plt.ylabel("Amplitude", color='r')

Text(0, 0.5, 'Amplitude')

f1=abs(np.fft.fft(signals))
plt.stem(f1[:500])

<StemContainer object of 3 artists>

Jay method trying with random signal

import librosa
file_path = 'Forest.wav'
samples , sampling_rate = librosa.load(file_path, sr = None, mono = True, offset = 0.0, duration = None)
len(samples), sampling_rate

(206388, 44100)

pip install librosa

Requirement already satisfied: librosa in c:\programdata\anaconda3\lib\site-packages (0.8.1)
Requirement already satisfied: joblib>=0.14 in c:\programdata\anaconda3\lib\site-packages (from librosa) (1.0.1)
Requirement already satisfied: audioread>=2.0.0 in c:\programdata\anaconda3\lib\site-packages (from librosa) (2.1.9)
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Note: you may need to restart the kernel to use updated packages.

import librosa
from librosa import display
plt.figure()
librosa.display.waveplot(y = samples, sr = sampling_rate)
plt.xlabel("Time in seconds")
plt.ylabel("Amplitude")
plt.show()

samples = 100
f = 3
x = np.arange(samples)
y1 = np.sin(2*np.pi*f * (x/samples))
plt.figure()
plt.stem(x,y1,  'r', )
plt.plot(x,y1)
plt.xlabel("Time in seconds")
plt.ylabel("Amplitude")
plt.show()

samples = 100
f = 11
x = np.arange(samples)
y2 = 2 * np.sin(2*np.pi*f * (x/samples))
plt.figure()
plt.stem(x,y2,  'r', )
plt.plot(x,y2)
plt.xlabel("Time in seconds")
plt.ylabel("Amplitude")
plt.show()

#Y3 will represent the resultant signal 
y3 = y1 + y2
plt.plot(y3)

[<matplotlib.lines.Line2D at 0x1f886ef14f0>]

#FFT plot
import scipy
def fft_plot(audio, sampling_rate):
    n = len(audio)
    T = 1/sampling_rate
    yf = scipy.fft(audio)
    xf = np.linspace(0.0, 1.0/(2.0*T), n/2)
    fig, ax = plt.subplots()
    ax.plot(xf, 2.0/n * np.abs(yf[:n//2]))
    plt.grid()
    plt.xlabel("Frequency")
    plt.ylabel("Magnitude")
    return plt.show()
    return xf
    return yf

# import required library
import numpy as np
import scipy.signal as signal
import matplotlib.pyplot as plt

# Given
f1 = 25 # Frequency of 1st signal
f2 = 50 # Frequency of 2nd signal
N = 10 # Order of the filter


t = np.linspace(0, 1, 1000)


sig = np.sin(2*np.pi*f1*t) + np.sin(2*np.pi*f2*t)

# Display the signal
fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
ax1.plot(t, sig)
ax1.set_title('25 Hz and 50 Hz sinusoids')
ax1.axis([0, 1, -2, 2])


sos = signal.butter(50, 35, 'lp', fs=1000, output='sos')


filtered = signal.sosfiltfilt(sos, sig)


# Display the output signal
ax2.plot(t, filtered)
ax2.set_title('After 35 Hz Low-pass filter')
ax2.axis([0, 1, -2, 2])
ax2.set_xlabel('Time [seconds]')
plt.tight_layout()
plt.show()

# import required library
import numpy as np
import scipy.signal as signal
import matplotlib.pyplot as plt

# Given
f1 = 25 # Frequency of 1st signal
f2 = 50 # Frequency of 2nd signal
N = 10 # Order of the filter


t = np.linspace(0, 1, 1000)


sig = np.sin(2*np.pi*f1*t) + np.sin(2*np.pi*f2*t)

# Display the signal
fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
ax1.plot(t, sig)
ax1.set_title('25 Hz and 50 Hz sinusoids')
ax1.axis([0, 1, -2, 2])


sos = signal.butter(50, 35, 'hp', fs=1000, output='sos')


filtered = signal.sosfiltfilt(sos, sig)


# Display the output signal
ax2.plot(t, filtered)
ax2.set_title(' After 35 Hz High-pass filter')
ax2.axis([0, 1, -2, 2])
ax2.set_xlabel('Time [seconds]')
plt.tight_layout()
plt.show()

Jay method trying with data given

#frequency domain representation
fourierTransform = np.fft.fft(signals)/len(signals)           # Normalize amplitude
fourierTransform = fourierTransform[range(int(len(signals)/2))] # Exclude sampling frequency

tpCount     = len(signals)
values      = np.arange(int(tpCount/2))
timePeriod  = tpCount/fs
frequencies = values/timePeriod

plt.plot (frequencies, abs(fourierTransform))
plt.title('Fourier transform depicting the frequency components')
plt.ylabel('Amplitude',color = 'r')
plt.xlabel('Frequency',color = 'r')

Text(0.5, 0, 'Frequency')

plt.plot (data1)
plt.title('Signal Forest')
plt.ylabel('Amplitude',color = 'r')
plt.xlabel('Time',color = 'r')

Text(0.5, 0, 'Time')

from scipy.fftpack import fft

import scipy.io.wavfile as wavfile
import scipy
import scipy.fftpack as fftpk
import numpy as np
from matplotlib import pyplot as plt

fs1, data1 = wavfile.read("Forest.wav") 

FFT = abs(np.fft.fft(data1))
freqs = fftpk.fftfreq(len(FFT), (1.0/fs1))

plt.plot(freqs[range(len(FFT)//2)], FFT[range(len(FFT)//2)])
                                                        
plt.xlabel('Frequency (Hz)')
plt.ylabel('Amplitude')
plt.show()

pip install librosa

Requirement already satisfied: librosa in c:\programdata\anaconda3\lib\site-packages (0.8.1)Note: you may need to restart the kernel to use updated packages.
Requirement already satisfied: scikit-learn!=0.19.0,>=0.14.0 in c:\programdata\anaconda3\lib\site-packages (from librosa) (0.24.1)
Requirement already satisfied: numba>=0.43.0 in c:\programdata\anaconda3\lib\site-packages (from librosa) (0.53.1)

Requirement already satisfied: joblib>=0.14 in c:\programdata\anaconda3\lib\site-packages (from librosa) (1.0.1)
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Requirement already satisfied: audioread>=2.0.0 in c:\programdata\anaconda3\lib\site-packages (from librosa) (2.1.9)
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import numpy as np
from scipy.signal import butter,filtfilt

!pip install plotly

Requirement already satisfied: plotly in c:\programdata\anaconda3\lib\site-packages (5.5.0)
Requirement already satisfied: tenacity>=6.2.0 in c:\programdata\anaconda3\lib\site-packages (from plotly) (8.0.1)
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import chart_studio.plotly

import plotly.offline as pyoff
import plotly.graph_objs as go

import plotly.figure_factory as ff

# Filter requirements.
T = 10.0      
cutoff = 2     
nyq = 0.5 * fs 
order = 2      
n = int(T * fs) 

def butter_highpass(cutoff, fs, order=5):
    nyq = 0.5 * fs
    normal_cutoff = cutoff / nyq
    b, a = signal.butter(order, normal_cutoff, btype = "high", analog = False)
    return b, a

def butter_highpass_filter(data, cutoff, fs, order=5):
    b, a = butter_highpass(cutoff, fs, order=order)
    y = signal.filtfilt(b, a, data)
    return y

# Filter the data, and plot both the original and filtered signals.
y = butter_highpass_filter(data1, cutoff, fs1, order)
fig = go.Figure()
fig.add_trace(go.Scatter(
            y = data1,
            line =  dict(shape =  'spline' ),
            name = 'signal with noise'
            ))
fig.add_trace(go.Scatter(
            y = y,
            line =  dict(shape =  'spline' ),
            name = 'filtered signal (high pass)'
            ))
fig.show()

def butter_lowpass_filter(data, cutoff, fs, order):
    normal_cutoff = cutoff / nyq
    # Get the filter coefficients 
    b, a = butter(order, normal_cutoff, btype='low', analog=False)
    y = filtfilt(b, a, data)
    return y

import plotly.graph_objects as go
# Filter the data, and plot both the original and filtered signals.
y = butter_lowpass_filter(data1, cutoff, fs1, order)
fig = go.Figure()
fig.add_trace(go.Scatter(
            y = data1,
            line =  dict(shape =  'spline' ),
            name = 'signal with noise'
            ))
fig.add_trace(go.Scatter(
            y = y,
            line =  dict(shape =  'spline' ),
            name = 'filtered signal (low pass)'
            ))
fig.show()

High pass

fps = 1500
filtered_forest = butter_highpass_filter(data1, 10, fps)
plt.plot(filtered_forest)

[<matplotlib.lines.Line2D at 0x1f88d0f5d60>]

Low pass

fps = 1500
order=5
filtered_forest_1 = butter_lowpass_filter(data1, 10, fps, order)
plt.plot(filtered_forest_1)

[<matplotlib.lines.Line2D at 0x1f88d1f5fd0>]

fps = 1500
order=5
filtered_forest_1 = butter_lowpass_filter(data1, 10, fps, order)
wavfile.write('lowpass_filter.wav',fps,data1)

fps = 1500
order=5
filtered_forest = butter_highpass_filter(data1, 10, fps, order)
wavfile.write('highpass_filter.wav',fps,data1)

fs3,data3 = wavfile.read('lowpass_filter.wav')
Audio(data=data3,rate=fs3)

fs4,data4 = wavfile.read('highpass_filter.wav')
Audio(data=data4,rate=fs4)

Mam's Method

from scipy.io import wavfile
fs, data = wavfile.read(r'C:\Users\JAY GOYAL\Forest.wav')
Audio(data=data, rate=fs)

from IPython.display import Audio
Audio(data=data, rate=fs)

plt.plot(data)

[<matplotlib.lines.Line2D at 0x1f88b8588b0>]

#Importance of transforms
print("Sampling frequency[number of samples in 1 sec]: ", fs)

Sampling frequency[number of samples in 1 sec]:  44100

print("Length of audio file in samples: ",data.size)

Length of audio file in samples:  206388

print("Length of audio file in seconds: ",data.size/fs)

Length of audio file in seconds:  4.68

f5 = abs(np.fft.fft(data))
N = len(data)
k = np.arange(0,N)
FF = k*(fs/N)
plt.figure(figsize=(14,4))
plt.plot(FF,f5)

[<matplotlib.lines.Line2D at 0x1f88d5c0d00>]

f5 = abs(np.fft.fft(data))
N = len(data)
k = np.arange(0,N)
FF = k*(fs/N)
plt.figure(figsize=(14,4))
plt.plot(FF[0:int(len(f5)/2)],f5[0:int(len(f5)/2)])

[<matplotlib.lines.Line2D at 0x1f88da6e580>]

#Filter
fc = 1000
w = fc/(fs/2)
b,a = signal.butter(5,w,'low')
print(b,'\n',a)
output_data = signal.filtfilt(b,a,data)
plt.figure(figsize=(14,4))
plt.plot(output_data)
plt.title('data pass through low pass filter')
plt.xlabel('Amplitude', color='r')
plt.ylabel('Frequency', color='r')

[1.46896340e-06 7.34481698e-06 1.46896340e-05 1.46896340e-05
 7.34481698e-06 1.46896340e-06] 
 [ 1.         -4.53905152  8.26066093 -7.53334038  3.44208742 -0.63030945]

Text(0, 0.5, 'Frequency')

f6 = abs(np.fft.fft(data))
N = len(data)
k = np.arange(0,N)
FF = k*(fs/N)
plt.figure(figsize=(14,4))
plt.plot(FF[0:int(len(f6)/2)],f6[0:int(len(f5)/2)])

[<matplotlib.lines.Line2D at 0x1f88cb55400>]

from IPython.display import Audio
Audio(data=output_data, rate=fs)

#Filter
fc = 1000
w = fc/(fs/2)
b,a = signal.butter(5,w,'low')
print(b,'\n',a)
output_data_1 = signal.filtfilt(b,a,data)
plt.figure(figsize=(14,4))
plt.plot(output_data_1)
plt.title('data pass through high pass filter')
plt.xlabel('Amplitude', color='r')
plt.ylabel('Frequency', color='r')

[1.46896340e-06 7.34481698e-06 1.46896340e-05 1.46896340e-05
 7.34481698e-06 1.46896340e-06] 
 [ 1.         -4.53905152  8.26066093 -7.53334038  3.44208742 -0.63030945]

Text(0, 0.5, 'Frequency')

f6 = abs(np.fft.fft(data))
N = len(data)
k = np.arange(0,N)
FF = k*(fs/N)
plt.figure(figsize=(14,4))
plt.plot(FF[0:int(len(f6)/2)],f6[0:int(len(f6)/2)])

[<matplotlib.lines.Line2D at 0x1f88cbfa070>]

from IPython.display import Audio
Audio(data=output_data_1, rate=fs)

wavfile.write('highpassfilter.wav',fc,output_data_1)

wavfile.write('lowpassfilter.wav',fc,output_data)

Conclusion:

From this experiment we observed the frequency components of audio files using FFT and then filtered the low and high frequency components using low and high pass filter.